Now we specify the subalgebras and subspace in Proposition REF  in a more general context than in [1]}.
A connected linear Lie complex group \(G\)  can be represented as a semidirect product
\(B\rtimes L\) , where \(B\)  is simply connected solvable and \(L\)  is linearly complex reductive; see [2]} or [3]}. Fix such a decomposition. Recall that \(N\subset B\) ; see the proof of Lemma REF .
